In fabricating an electronic device such as a semiconductor device or a flat panel display, a fine pattern is formed on the surface of a substrate (for example, a wafer or the like) by a photolithography process. In designing by such a photolithography process, what are mainly determined are: Illumination condition of an exposure apparatus, a pattern layout of a photomask, an advantageous pattern layout of a device to exposure, and so forth.
In recent years, patterns have become finer and the degree of fineness is approaching the resolution limit of an exposure apparatus. Accordingly, illumination conditions of an exposure apparatus are often set to be suitable for transferring the densest pattern (the finest pattern). Hence, in order to Improve the exposure latitude and depth of focus for patterns other than the densest pattern even under such illumination conditions of an exposure apparatus, there has been proposed a technique in which a fine assist pattern Is placed around a mask pattern (hereinafter, referred to as a design pattern) (for example, refer to JP-A 2002-323748 (Kokai)).
However, when the assist pattern is included, the number of conceivable pattern layouts for a photomask becomes enormous, making it extremely difficult to perform a comprehensive simulation. For this reason, a design is made according to an optimization method to obtain an optimal solution. Specifically, an assist pattern is placed based on the experience of a designer, and verification is repeated on the basis of the pattern layout.
By designing with the optimization method, a pattern layout including an assist pattern can be determined. Nevertheless, the method leads to increases in cost and time in designing. Moreover, the designing method has a difficulty in obtaining the optimal solution because the placement, size, number, and the like, of the assist pattern are determined based on the experience of a designer in a trial-and-error manner.
Against this problem, there has been proposed a technique for automatically placing an assist pattern under predetermined conditions around a design pattern by use of a computer (refer to JP-A 9-297388 (Kokai)(1997)).
According to the technique disclosed in JP-A 9-297388 (Kokai)(1997), an assist pattern can be placed within practical time and cost.
However, when multiple assist patterns are simply placed, the lithographic latitude (the exposure latitude and depth of focus) may be reduced due to interaction among the assist patterns.